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Journals / Hacettepe Journal of Mathematics and Statistics / 2018 / Cilt: 47 - Sayı: 4

Basic sequences and unbiased estimation in quasi power series distributions

Faqir MUHAMMAD
M. Kazim KHAN
Pages
877–887
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

This extends some knownresults in Bleimann, Butzer and Hahn's approximation operator.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:By using results from function space theory we give a characterization of when lacunary quasi power series sequences are basic in $C[0, 1]$.
📊
Key Findings & Data:The paper discusses the links with unbiased estimable functions and the subspaces generated by the density of the lacunary quasi power series distributions.
💡
Conclusion & Impact:This extends some knownresults in Bleimann, Butzer and Hahn's approximation operator.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:UMVU estimators · unbiased estimators · lacunary sequences

Abstract

By using results from function space theory we give a characterization of when lacunary quasi power series sequences are basic in $C[0, 1]$. The paper discusses the links with unbiased estimable functions and the subspaces generated by the density of the lacunary quasi power series distributions. The paper also provides the rates of convergence of all the moments of the classic odds ratio estimator. This extends some knownresults in Bleimann, Butzer and Hahn's approximation operator.

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Cite This Article

MUHAMMAD, F., KHAN, M. K. (2022). Basic sequences and unbiased estimation in quasi power series distributions. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 4, 877–887. https://ajindex.com/articles/529845

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References (18)

  1. Berg, C. and Vignat, C. Linearization coffie cients of Bessel polynomials and properties of Student t-distribution, Constructive Approximation, 27, 1532, 2008.
  2. Bianchi, G. and Sorrentino, R. Electronic Filter Simulation and Design, (McGraw Hill, NY. 2007).
  3. Bleimann, G.; Butzer, P. L. and Hahn, L. A Bernstein-type operator approximating continuous functions on the semi-axis, Nederl. Akad. Wetensch. Indag. Math., 42, 255262, 1980.
  4. Della Vecchia, B. Some properties of a rational operator of Bernstein-type, In: Progress in Approximation Theory, 177185, (Academic Press, Boston, 1991).
  5. En o, Per. A counter example to the approximation problem in Banach spaces, Acta Math- ematica, 130 (1), 309317, 1973.
  6. Gurariy, V.I. and Matsaev, V.I. Lacunary power sequence in the spaces $C$ and $L_p$, Izv. Akad. Naud SSR Ser. Mat. 30, 314, 1966 (in Russian). Amer. Math. Soc. Trans. 72, 921, 1968 (in English). Gurariy, V.I. and Lusky, W. Geometry of Müntz Spaces and Related Questions, Lect. Notes Math. 1870, Springer-Verlag, Berlin, 2005.
  7. Joshi, S.W. and Park, C.J. Minimum variance unbiased estimation for truncated power series distribution, Sankhya: The Indian Journal of Statistics, Series A, 36(3), 305314, 1974.
  8. Khan, R. A. A note on a Bernstein-type operator of Bleimann, Butzer and Hahn, J. Approx. Theory, 53, 295303, 1988.
  9. Khan, R. A. Reverse martingales and approximation operators, J. Approx. Theory, 80, 367377, 1995.
  10. Khatri, C.G. On certain properties of power series distributions, Biometrika, 46, 486490, 1959.
  11. Krall, H. L., and Fink, O., A new class of orthogonal polynomials: The Bessel polynomials, Trans. Amer. Math. Soc., 65, 100115, 1948.
  12. Lehmann, E. L. and Casella, George. Theory of Point Estimation, 2nd ed. (Springer-Verlag, N.Y. 1998).
  13. Noack, A. A class of random variables with discrete distributions, Ann. Math. Stat. 21, 127132, 1950.
  14. Patil, G. P. Minimum Variance Unbiased Estimation and Certain Problems of Additive Number Theory, Ann. Math. Stat. 34, 10501056, 1963.
  15. Patil, G. P. and Joshi, S. W. Further Results on Minimum Variance Unbiased Estimation and Additive Number Theory, Ann. Math. Stat. 41(2), 567575, 1970.
  16. Patil, G. P. and Wani, J. K. On Certain Structural Properties of the Logarithmic Series Distribution and the First Type Stirling Distribution, Sankhya: The Indian Journal of Sta- tistics, Series A, 27(2/4), 271280, 1965.
  17. Plackett, R. L. The truncated Poisson distribution, Biometrics, 9, 485488, 1953.
  18. Tate, R. F. and Goen, R. L. Minimum V